Yes, possible long term, but only if one can create the fuels. That's highly doubtful without retarting up an existing gasline and have technicians to operate/maintain it.I doubt that oil drilling into fuels would occur based upon the complexity of restarting a refinery. The only possible gas that I can think possible post-collapse on a small scale is biogas (methane). This need warmth, so of lesser use in temperate zones for digestion of waste material by bacteria, but regular creation can occur in tropical zones.

There's evaporative cooling like swamp coolers which are an old style that were used in air conditioning but require electricity which goes probably back to wood-gasification into generators to get that. It's why a Zeer pot will work for tiny but important refrigeration for preventing spoiliage of some items.

The most likely kind of refrigeration, but only to an average 50 deg F (10 deg C) is a root cellar.

There's lots of exotic kinds of refrigeration, but these require chemicals to draw from, and hence likely impossible long term. You're much more optimistic than I am about restarting civillization.